1. Field of the Invention
The present invention relates generally to optical metrology and more particularly to methods for the determination of intra-field distortion and lens aberrations for projection imaging systems used in semiconductor manufacturing.
2. Description of the Related Art
Semiconductor manufacturers and lithography tool vendors have been forced to produce higher numerical aperture (NA) lithography systems (steppers or scanners) using smaller wavelengths (for example, 193 nm DUV lithography) in response to the semiconductor industry's requirement to produce ever-smaller critical features. See, for example, the statement of the well-known “Moore's Law” at “Cramming More Components Onto Integrated Circuits”, G. Moore, Electronics, Vol. 38, No. 8, 1965. The ability to produce (manufacture) sub-wavelength features can often be determined by considering the rather simple (3-beam) Rayleigh scaling Resolution (R) and Depth-of-Focus (DoF) equations: ˜λ/2NA and ˜λ/2NA2. See “Introduction to Microlithography”, L. Thompson et al., ACS, 2nd Edition, 1994, p. 69. These coupled equations stress the inverse relationship between resolution and DoF based on the exposure wavelength (λ and numerical aperture (NA), for features printed near the limit of the optical system. High NA lithography (including immersion lithography) has led to improved resolution and a reduction in the overall focus budget, making lithography processes difficult to control. See “Distinguishing Dose from Defocus for In-line Lithography Control”, C. Ausschnitt, SPIE, Vol. 3677, pp. 140:147, 1999, and “TWINSCAN 1100 Product Literature” ASML. In addition, the push for faster product development, reduced cycle time, and better cost management often means that photolithographic exposure tools (steppers and scanners) are pushed beyond performance specifications, where lens aberrations and exposure source variations become critical to monitor and understand. See “Impact of Lens Aberrations on Optical Lithography”, T. Brunner, IBM, Vol. 41, pp. 1:2, 1997 (available at the URL of www.research.ibm.com). Aberrations (wave front deviation), defined as the deviation of the real performance of a projection lens from ideal performance, can be mathematically formulated a number of ways, but in each case the result is a mathematical description of the phase error across the lens pupil. See, for example, “Basic Wavefront Aberration Theory for Optical Metrology”, J. Wyant, K. Creath, ISBN 0-12-408611-X, Chapter 1, pp. 1-53, 1992. Lens aberrations are typically responsible for both local (field dependent) transverse error (feature-shift) and critical dimension variation (feature shape error). The present discussion will be concerned with aberrations responsible for transverse error, stemming from both source and lens. We use a rather general Zernike aberration convention, where A0, 0, 1 and A0, 0, −1 (or a2 and a3) are the Zernike x-tilt, y-tilt coefficients, where A0, 3, −1 and A0, 3, 1 (or a8 and a7) are the Zernike coma-x, coma-y coefficients, and where O(ax) represents higher order aberrations, each of which is responsible for some portion of transverse distortion and possibly other effects. Several methods exist for determining transverse distortion as function of field position using overlay metrology. See “Analysis of Overlay Distortion Patterns”, J. Armitage, J. Kirk, SPIE, Vol. 921, pp. 207:221, 1988, “Method and Apparatus for Self-Referenced Projection Lens Distortion Mapping, A. Smith et al., U.S. Pat. No. 6,573,986 issued Jun. 3, 2003, and “Method and Apparatus for Self-Referenced Dynamic Step and Scan Intra-Field Lens Distortion”, A. Smith, U.S. patent application Ser. No. 10/252,020 filed Sep. 20, 2002. However, the ability to precisely determine the Zernike coefficients (a2 and a3) depends on the ability to separate out the distortion effects of (low order) coma since both aberrations give rise to feature-shift. The third-order coma (x-coma, y-coma or both), or the effects from third-order coma, can occur when image contributions from different pupil radii shift relative to one another, as described by Equation 1 below, a generalized Zernike polynomial (of the third-order) for the optical path difference (OPD):OPD(Z7, Z8)=factor*(3ρ3−2ρ*sin(φ), cos(φ) or factor*(3ρ2−2)*Z2, Z3  (Eq. 1)where Z8, Z7 represent the Zernike polynomials for x-coma and y-coma, ρ is the exit pupil radius, φ is the angular position in the pupil, and Z2, Z3 represent the Zernike polynomials for x and y field tilt. See “Impact of Lens Aberrations on Optical Lithography”, supra, for discussion of Zernike polynomials.
Equation 1 shows clearly that rays (for geometric descriptions) passing near the center of the pupil deviate differently than rays near the edge of the pupil. These ray deviations cause both CD variation (asymmetric feature patterns) and feature-shift. The variation in phase across the exit pupil in the presence of x-coma, for example, is shown in FIG. 1a. Since most photolithographic exposure tools allow for different source shapes, the feature dependent shift is also a function of source shape and varies slowly across the exposure field or scanning slot. In the presence of coma, a small pin hole (opening<<transverse resolution) on a reticle is imaged into a comet-type object, as shown in FIG. 1b. Finally, since lithographic features are created by the complex superposition of many small aberrated point sources, the resulting feature shapes generally depend on both the size and orientation of the reticle patterns.
Detailed and accurate knowledge of the aberrations (especially those related to transverse distortion) can be fed directly into (inter and intra-field) overlay modeling and control routines to improve overlay performance, since the overlay control models (for example, models such as Klass II and Monolith) require understanding of all sources of distortion or transverse displacement. See “Analysis of Overlay Distortion Patterns”, supra, and “Mix-and-Match: A Necessary Choice”, R. DeJule, Semiconductor International, pp. 66:76, February 2000. Overlay registration, or misregistration, is the translational (positional) error that exists between features exposed layer to layer in the vertical fabrication process of semiconductor devices on silicon wafers. Typically, alignment attributes or overlay targets are used to determine the magnitude of the error (see FIGS. 2a-2b). Other names for overlay registration include registration error and pattern placement error; for this description, the terms “overlay error” or “error” will be used. An overview of overlay modeling and control schemes can be found in “Analysis of Overlay Distortion Patterns”, supra, “Measuring Fab Overlay Programs”, R. Martin et al., SPIE Metr. Inspection, and Process Control for Microlithography, XIII, pp. 64:71, March 1999, and “Method for Overlay Control System”, C. Ausschnitt et al., U.S. Pat. No. 5,877,861 issued Mar. 2, 1999. Finally, in addition to lateral shifts, distortion related aberrations are also responsible for degrading image fidelity (or modulation), proportional to the variance of the distortion along the scanning direction. Given details of the lens distortion, those of skill in the art can generally make changes in the configuration of the slit geometry and improve imaging performance.
There are various sources of overlay error for both targets and patterned features. See, for example, “The Waferstepper Challenge: Innovation and Reliability Despite Complexity”, Gerrit Muller, Embedded Systems Institute Netherlands, pp. 1-10, 2003. These overlay error sources include reticle (tilt, pattern misplacement, warp), source (telecentricity, source settings), overlay mark fidelity, feature dependent processing error, wafer (topography, flatness), lens (aberrations, telecentricity), stage (static and dynamic stage error global alignment), overlay measurement (tool induced shift, precision), and tool matching (stage, lens, matching accuracy). See, for example, “Thinking Outside the Box for Improved Overlay Metrology”, I. Pollentier et al., SPIE Microlithography Proceedings, Vol. 5038, pp. 12:16, 2003, and “Method and Apparatus for Self-Referenced Dynamic Step and Scan Intra-Field Scanning Distortion”, A. Smith, U.S. patent application Ser. No. 10/252,021 filed Sep. 20, 2002. It is interesting to note that the overlay error associated with large feature alignment attributes only approximates the overlay error associated with the actual printed circuit features since features for a variety of reasons including: size differences, pattern placement error, inherent overlay mark error, source/aberration coupling.
Over the past 30 years the microelectronics industry has experienced dramatic rapid decreases in critical dimension (feature-size) by constantly improving photolithographic imaging systems and developing new reticle enhancement techniques. See, for example, “Resolution Enhancement with OPC/PSM”, F. Schellenberg, Future Fab International, Vol. 9, 2000. Photolithographic imaging systems are often pushed to and beyond performance limits. As the critical dimensions of semiconductor devices approach 50 nm (and below), the overlay error requirements will soon approach atomic dimensions, making overlay process control extremely difficult. See “International Technology Roadmap for Semiconductors, 2001 Edition”, SEMATECH, pp. 1-21. New methods for identifying and quantifying the sources of overlay error will become vital. In particular, methods for accurately determining lens aberrations (especially low order distortion) and source irregularity and their coupled effects on image fidelity and overlay will remain critical. Finally, another area where quantifying distortion error is of vital concern is in the production of photomasks (and direct-write lithography) during the electron beam (including; laser, multi-mirror, ion-beam) manufacturing processes. See “Handbook of Microlithography, Micromachining, and Microfabrication”, P. Rai-Choudhury, SPIE Press, Microlithography, Vol. 1, pp. 417, 1997.
Aberration and Source
Some examples of typical illumination source or illumination geometry for photolithographic imaging systems are illustrated in FIG. 3. Several good references on aberrations and their effects on lithographic imaging can be found in the literature. See, for example, “Aberration Measurement of Photolithographic Lenses by Use of Hybrid Diffractive Photomasks”, J. Sung et al., Applied Optics, Vol. 42, No. 11, pp. 1987-1995, Apr. 10, 2003, and “Impact of Lens Aberrations on Optical Lithography”, supra. The effects of third-order coma on pattern shift are fairly well-known and numerical methods can be used to ray trace or model the behavior (determine pattern shift as a function of source shape, feature size and optical parameters) when the Zernike terms are known. In general, the coma aberration can be split into two terms, x-coma and y-coma. Where x-coma is responsible for shifting and/or degrading vertical features and y-coma shifts and/or degrades horizontal features. Since, in general, the Zernike polynomial expansion contains many significant terms (up to several hundred depending on the lens) it is hard to perform lithographic experiments that isolate the effects of one particular Zernike term, without complex assumptions. See, for example, “Experimental Assessment of Pattern and Probe-Based Aberration Monitors”, G. Robins, A. Neureuther, SPIE, Microlithography Proceedings, Vol. 5040-149, pp. 1:12, 2003, and “Aberration Measurement of Photolithographic Lenses by Use of Hybrid Diffractive Photomasks”, supra. One method of determining the Zernike coefficients using an in-situ interferometer is described in “Apparatus, Method of Measurement and Method of Data Analysis for Correction of Optical System”, A. Smith et al., U.S. Pat. No. 5,828,455 issued Oct. 27, 1998.
Distortion
A conventional method for determining lens distortion in the presence of aberrations (FIG. 1c) is described in “Analysis of Image Field Placement Deviations of a 5× Microlithographic Reduction Lens”, D. MacMillen et al., SPIE Vol. 334, pp. 78-89, 1982, where it is tactically assumed that the stepper or scanner wafer stage moves in a nearly perfect manner. Under the assumptions of a perfect wafer stage (stage error small and randomly distributed) one prints a large array of box-targets or alignment attributes (FIG. 2a) across the exposure field. Next, the stepper or scanner is programmed to step and print one small overlay target box inside each of the previously imaged field points (creating readable alignment attributes or a box-in-box target) using a constant aberration portion of the lens. One then determines (estimates) the lens distortion by measuring the feature-shift of the array (FIG. 1d) using an optical metrology tool and several modeling equations that account for additional overlay errors and statistical fluctuations. See, for example, “Measuring Fab Overlay Programs”, supra, “KLA 5105 Overlay Brochure”, KLA-Tencor, “Quaestor Q7 Brochure”, Bio-Rad Semiconductor Systems, and “Measuring Fab Overlay Programs”, supra. In general, it is common to ignore the effects of third-order or higher coma on large-feature-shift and to assume that the large-pattern shifts are entirely due to the effects of Zernike tilt terms of low order (a2 and a3 for example) or other easily modeled global shifts. In fact, as mentioned previously, even semiconductor fab overlay procedures disregard the effects of coma on overlay targets altogether.
Several preferred methods for determining lens distortion for steppers (or scanners) are described by A. Smith in U.S. patent application Ser. No. 10/252,021, supra, U.S. patent application Ser. No. 10/252,020, supra, and U.S. Pat. No. 6,573,986, supra. Smith describes a sequence of lithographic exposures and measurements using a novel reticle pattern to mathematically solve for lens distortion in the presence of stage noise and synchronization error. In addition, these preferred methods can be used to determine the Zernike tilt coefficients (a2 and a3) by subtracting off the effects of third-order (or higher order aberrations) if the aberrations for the lens are known. If the aberrations are not known then techniques such as those described by U.S. Pat. No. 5,828,455 can be used to determine the Zernike coefficients (x-coma and y-coma a8 and a7 for example) as a function of field position for both steppers and scanners. Once the coma coefficients are known (as a function of field position), a2 and a3 can be determined by subtraction.
For the preferred methods such as described in U.S. patent application Ser. No. 10/252,020, supra or U.S. Pat. No. 6,573,986, supra, lens distortion is determined by measuring arrays of alignment attributes (using standard overlay methods), solving a complex system of equations and then subtracting off both global and statistical sources of error. The results for lens distortion can be reduced to a simple linear combination of X, Y tilt and X, Y primary (third-order) coma, where higher order contributors are ignored. This relationship is shown in Equation 2.(DX, DY)=(a2*dX/da2+a8*dX/da8, a3*dY/da3+a7*dY/da7)  (Eq. 2)where:                DX, DY represent field dependent pattern shifts as determined by the technique of U.S. patent application Ser. No. 10/252,020, supra, U.S. Pat. No. 6,573,986 and the like;        a2, a3 are Zernike x-tilt and y-tilt coefficients, each a function of field position;        a7, a8 are primary Zernike y-coma and x-coma coefficients, each a function of field position;        dX/da2=dX/da3=(x,y) tilt shift coefficients=−λ/na*π;        dX/da8, dY/da7=(x,y) coma shift coefficients=complex function of source shape and feature pattern; and        λ, NA=projection tool wavelength, exit pupil NA        
In general, if the coma coefficients a7 and a8 are known (across the exposure field or slot) one then calculates (simulates) feature-shift versus coma coefficient (a7, a8 or both) for a given source shape and feature-size and arrives at a good estimate of dX/da8 and dY/da7. Then, a2 and a3 can be estimated by manipulation of Equation 2.a2, a3=[(DX−a8*dX/da8)/(dX/da2),(DY−a7*dY/da7)*dY/da3)].  (Equation 3)
While several methods are known for determining lens distortion, an improved determination of lens distortion can be obtained if the cross coupling effects of third-order coma and tilt on transverse distortion are reduced or eliminated. These known methods would need knowledge of the Zernike coefficients (especially third-order coma) as a function of field position to eliminate the cross coupling effects of third-order coma and tilt on transverse distortion. Therefore, it would be desirable to have a process for determination of a2 and a3 in the presence of low order coma aberrations when it is not possible or convenient to determine a complete set of Zernike coefficients for a lens system and process.